The word you are looking for is enthnicity. Enthnicity describes the (self-)perceived belonging to a population group. This is of course highly subjective.
There is undeniably perception of grouping in the US based on heritage, where it doesn’t really matter when your ancestors arrived, just from where. So from an American POV it makes sense to call him Italian, because he is in the same perceived group as all the people from Italy.
On the other hand from a European POV it doesn’t really matter, where your great grandparents come from. You are part of the US-Group, so you are American.
This is not an exclusive US Problem, but a general migration problem & it happens everywhere. Comments like yours are the reason, why people from migrated families feel like they are in-between cultures. Instead of writing snarky comments on the internet, just accept that your perception of ethnicity is part of your ethnicity and other people can have other perceptions.
Other than the medieval church, global academia has the fundamentals right, imho. The methods are flawed but the general goal is the right one.
The problem in the US is not a fundamental flaw in academia, but lack of political understanding that a state benefits from educated citizens and fundamental research that isn’t immediately monetisable. That resulted in this weird situation, where the most prestigious facilities are just sport centers with a side hustle in education.
In the future the methods of today’s global research will more likely be seen as something like greek philosophers. The goal of generating knowledge was right. The method of just writing down what your two remaining neurons, that haven’t drowned in wine yet, produced and never verifying it, was… let’s call it flawed from a modern perspective.